How does the continuity equation explain jet engine thrust?

[Penn_State21]

I have this one as well, using the continuity equation to explain how a jet engine provides a foward thrust for an airplane. I have the equation but can some one explain this to me in laymen's terms.

$$\frac{\partial\rho\left(\vec{r},t\right)}{\partial t}+\nabla\cdot\left[\rho\left(\vec{r},t\right)\vec{v}\left(\vec{r},t\right)\right]= 0$$

Thanks in advance for your help.

Kris

 

[Astronuc]

The continuity equation is an equation related to conservation of mass.

The rate of change of density (in a constant volume) is equal the net mass flux across the boundary of a differential volume.

If the net flux is zero, i.e. the mass flow in = mass flow out, then there is no change in density (and no accumulation or decrease in mass) in a fixed volume.